Low voltage crystal oscillator (XTAL) driver with feedback controlled duty cycling for ultra low power

ABSTRACT

A low voltage crystal oscillator (XTAL) driver with feedback controlled duty cycling for ultra low power biases an amplifier for an XTAL in the sub-threshold operating regime. A feedback control scheme can be used to bias the amplifier for an XTAL biased in the sub-threshold operating regime. The amplifier of a XTAL oscillator can be duty cycled to save power, e.g., the XTAL driver can be turned off to save power when the amplitude of the XTAL oscillation reaches a maximum value in range; but be turned back on when the amplitude of the XTAL oscillation starts to decay, to maintain the oscillation before it stops. In addition or alternatively, a feedback control scheme to duty cycle the amplifier of a XTAL oscillator can be used to monitor the amplitude of the oscillation.

PRIORITY CLAIMS

This application is a continuation of U.S. application Ser. No.15/161,521 entitled “A Low Voltage Crystal Oscillator (XTAL) Driver WithFeedback Controlled Duty Cycling For Ultra Low Power,” filed May 23,2016, which is a continuation of U.S. application Ser. No. 14/594,814entitled “A Low Voltage Crystal Oscillator (XTAL) Driver With FeedbackControlled Duty Cycling For Ultra Low Power,” filed Jan. 12, 2015, whichis a non-provisional of U.S. Provisional Application Ser. No.61/926,014, entitled “A Low Voltage Crystal Oscillator (XTAL) DriverWith Feedback Controlled Duty Cycling For Ultra Low Power,” filed Jan.10, 2014, the entire contents of which applications are all incorporatedherein by reference.

FIELDS

Some embodiments generally relate to low power circuit designs, and moreparticularly, relate to a low voltage XTAL driver with feedbackcontrolled duty cycling for ultra low power.

BACKGROUND

Portable systems that operate from a battery and/or from power harvestedfrom the environment typically need to consume small amounts of energyto prolong the system lifetime for a given amount of available energy.The energy budget for a portable system is increasingly important in awidening set of applications due to a combination of requirements forsmaller size (less battery volume, so less energy available), longerlifetimes (make energy last longer), and/or more functionality (do morewith the same amount of energy).

Many portable electronic devices such as wireless sensor nodes furthertypically spend a large fraction of their time in sleep modes waitingfor external or internal stimuli to awaken them. During these sleep (orstandby) modes, many devices use a stable clock source for keeping timeto reduce the cost of re-synchronizing to other radios, among otherreasons. During active modes, an accurate timing reference is used forbias precise data sampling, RF modulation, and synchronous digitalcomputation, among other reasons.

One known approach to provide an accurate clock source includes using acrystal oscillator (XTAL). XTAL-based oscillators can consume anappreciable portion of available system power, especially during standbymodes. For example, an energy harvesting body sensor network (BSN) SoC(system on a chip) having a 200 kHz XTAL consumes 19 μW while measuringECG, extracting heart rate, and sending RF packets every few seconds. F.Zhang, Y. Zhang, J. Silver, Y. Shakhsheer, M. Nagaraju, A. Klinefelter,J. Pandey, J. Boley, E. Carlson, A. Shrivastava, B. Otis, and B. H.Calhoun, “A Battery-less 19 μW MICS/ISM-Band Energy Harvesting Body AreaSensor Node SoC,” ISSCC Dig. Tech. Papers, pp.298-299, 2012, which isincorporated by reference. In this example, over 2 μW of the total powerconsumption is consumed by the 200 kHz XTAL. Id.

Thus, a need exists for a method to produce an accurate clock signalfrom a XTAL oscillator at much lower power levels that are compatiblewith miniaturized ultra low power electronics.

SUMMARY

Systems, methods, and apparatus for operating a crystal oscillator(XTAL) at very low voltage, e.g., even into the sub-threshold operatingregime of the metal-oxide-semiconductor (MOS) transistors, aredescribed. In some embodiments, a calibration scheme optimizes the XTALdriver for operation at low voltages. To achieve further power savings,the XTAL driver can include a feedback-controlled mode that duty cyclesthe XTAL while maintaining a stable output clock. Some embodimentsdisclosed herein include an apparatus that has a XTAL driver, which hasan amplifier with MOS transistors. The XTAL driver is configured toproduce an operating signal to operate a XTAL while the MOS transistorsare operated at a sub-threshold operating regime. The apparatus alsoincludes a feedback control unit that is operatively coupled to the XTALdriver. The feedback control unit is configured to receive the operatingsignal from the XTAL driver, the feedback control unit configured togenerate an adjustment signal based on the operating signal. The XTALdriver is further configured to adjust circuit level properties of theXTAL driver in response to the adjustment signal such that a negativeresistance of the amplifier of the XTAL driver is calibrated to a valuefor operation of the MOS transistors at the sub-threshold operatingregime.

Some embodiments disclosed herein include an apparatus that has a XTAL,which is configured to operate at a sub-threshold operating regime ofMOS transistors to generate an oscillation. The apparatus furtherincludes a XTAL driver communicatively coupled to the XTAL, which isconfigured to generate a duty cycle signal to modulate an envelope ofthe oscillation. The apparatus further includes a feedback control unitcommunicatively coupled to the XTAL driver and the XTAL, which isconfigured to use feedback from the oscillation to repeatedly turn onthe XTAL driver when an amplitude of the envelope of the oscillationdecays to a minimum value and turn off the XTAL driver when theamplitude of the envelope of the oscillation reaches a maximum value.

Some embodiments disclosed herein include a method for duty cycling aXTAL. The method performs the following: obtaining measurements of arise time and a fall time of a XTAL oscillation envelope; sending aninitiation signal to the XTAL to initiate an XTAL oscillation that isconfigured to reach a maximum amplitude; and repeatedly performing:sending a first signal to turn off the XTAL driver for a first timeproportional to the fall time of the XTAL oscillation envelope, andsending a second signal to turn on the XTAL driver for a second timeproportional to the rise time of the XTAL oscillation envelope. Thefirst time and the second time are relative to growing and decayingdelays of the XTAL oscillation envelope such that the XTAL oscillationis preserved.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing a known XTAL circuit and its equivalentcircuit schematic.

FIG. 2 shows a block diagram of a feedback scheme that uses informationfrom the output of a XTAL driver operating at low voltage, includinginto the sub-threshold region, according to an embodiment.

FIG. 3 is a block diagram of a system that can use a calibration methodto size the XTAL driver for operation at very low supply voltages,according to an embodiment.

FIG. 4 is a block diagram of a system that can use a calibration circuitthat sizes the XTAL driver for operation at very low supply voltages,according to an embodiment.

FIG. 5 shows a circuit diagram of an example of the calibration circuitthat sizes the XTAL driver for operation at very low supply voltages,according to an embodiment.

FIG. 6 is an example of simulation result that shows proper startup ofone instantiation of a low voltage XTAL driver with a supply voltage of300 mV.

FIG. 7 shows a system block diagram for a XTAL driver and feedbackcontrol scheme that uses feedback from the oscillating signal(s) X_(I)and/or X_(O) to turn on and off the driver for saving power, and atiming diagram showing how duty cycling can modulate the envelope ofX_(I) (and X_(O)) without stopping oscillation if the duty cycle iscontrolled relative to the amplitude of the X_(I) envelope, according toan embodiment.

FIG. 8 shows a system block diagram for a system that can control theduty cycle of the XTAL driver by turning it on and off and a timingdiagram showing how duty cycling can modulate the envelope of XI withoutstopping oscillation if the duty cycle is controlled relative to thegrowing and decaying delays (T_(G) and T_(D), respectively) of the X_(I)envelope, according to an embodiment.

FIG. 9 shows a block diagram of a circuit to measure the rising delay,T_(G), of the oscillation envelope of X_(I), according to an embodiment.

FIG. 10 shows a block diagram showing a circuit to measure the fallingdelay, T_(D), of the oscillation envelope of X_(I), according to anembodiment.

FIG. 11 shows a circuit schematic of an example of the complete XTALoscillator system.

FIG. 12 shows an example of simulations results of the X_(O) waveformshowing the envelope during duty cycled operation and the enable signalwaveform.

FIG. 13 shows a flowchart for calibrating an XTAL driver for operationat low voltage including the sub-threshold region, according to anembodiment.

FIG. 14 shows a flowchart for duty cycling the driver for an XTAL whilepersevering oscillation, according to an embodiment.

FIG. 15 shows a flowchart for duty cycling an XTAL while perseveringoscillation, according to another embodiment.

DETAILED DESCRIPTION

The low voltage crystal oscillator (XTAL) driver with feedbackcontrolled duty cycling for ultra low power bias an amplifier for anXTAL in the sub-threshold operating regime. Alternatively, a feedbackcontrol scheme can be used to bias the amplifier for an XTAL biased inthe sub-threshold operating regime.

In some embodiments, the amplifier of a XTAL oscillator can be dutycycled to save power. For example, a XTAL driver (e.g., the amplifier105, which includes metal-oxide-semiconductor (MOS) transistors) can beturned off to save power when the amplitude of the XTAL oscillationreaches a maximum value in range but be turned back on when theamplitude of the XTAL oscillation starts to decay. This allows the XTALoscillator to maintain the oscillation before it stops. In addition oralternatively, a feedback control scheme to duty cycle the amplifier ofa XTAL oscillator can be used to monitor the amplitude of theoscillation.

FIG. 1 shows the architecture (e.g., 101) and equivalent circuit (e.g.,102) for a known XTAL implementation for oscillation in parallel mode.In parallel mode, the crystal oscillator XTAL 106 appears as an inductor109 and oscillates with the load capacitors C_(L) 112. The equivalentcircuit of the XTAL itself is a series RLC circuit with a parallelparasitic capacitance Cp 113. The quality factor (Q) of a crystaloscillator is in the range of 50,000, which provides a precise frequencyoutput. The inverting amplifier 105 presents a negative resistance 108to the applied ac current to overcome the damping effect of crystal'sequivalent series resistance (ESR) 111 in the RLC circuit of FIG. 1. Tooscillate, the circuit can meet the Barkhausen criteria of oscillationby making the negative resistance 108 of the amplifier greater than theESR 111 of the crystal. The value of the negative resistance 108 is afunction of frequency. The ESR 111 of the crystal represents an energydissipating component, and the amplifier 105 compensates for thisdissipation through its negative resistance 108 bysupplying/replenishing the dissipated energy in the crystal.

The power consumption of the XTAL circuit is determined by the XTAL 106and the design of the amplifier 105. The energy dissipating component incrystal oscillator 106 represented by is the crystal's ESR 111. ESR 111represents the dissipation of energy in the form of heat loss and isgiven by I²R, where R is the value of resistance of the crystal's ESR111, and I is the RMS (Root Mean Square) current flowing into thecrystal. This loss is directly proportional to the amplitude ofoscillation. To reduce the loss and hence to reduce the powerconsumption of the crystal oscillator 106, often the amplitude ofoscillation is reduced. This can be done by operating the amplifier 105in sub-threshold region. E. Vittoz, and J. Fellarath, “CMOS AnalogIntegrated Circuits Based on Weak Inversion Operations,” IEEE Journal ofSolid State Circuits, vol. 12 no. 3 pp 224-231 Jun. 1977; and W.Thommen, “An improved Low Power Crystal Oscillator,” IEEE European SolidState Circuits Conference, 1999; each of which is incorporated byreference. Known circuit techniques reduce the amplitude of oscillationby using a delay locked loop (DLL) or by simply quenching theoscillation amplitude. D. Yoon, D. Sylvester, and D. Blaauw, “A 5.58 nW32.768 kHz DLL-Assisted XO for Real-Time Clocks in Wireless SensingApplications” IEEE International Solid State Circuits Conference, 2012;W. Thommen, “An improved Low Power Crystal Oscillator,” IEEE EuropeanSolid State Circuits Conference, 1999; each of which is incorporated byreference. These techniques have reduced the power consumption of 32 kHzcrystal oscillator to 5.58 nW making it possible to use the crystaloscillator for wireless sensors, where a lower power clock is desired.

In contrast to these known circuit techniques, described herein aresystems, methods, and apparatus for operating a crystal oscillator(XTAL) at very low voltage, even into the sub-threshold operating regimeof the MOS transistors (of the amplifier 105 for example). In someembodiments, calibration scheme optimizes the XTAL driver (e.g., theamplifier 105) for operation at low voltages. To achieve further powersavings, the XTAL driver can include a feedback controlled mode (notshown in FIG. 1; see 202 in FIG. 2, 303 in FIG. 3, 403 in FIG. 4, etc.)that duty cycles the XTAL 106 while maintaining a stable output clock.

As discussed further below, a compensated amplifier can maintainoscillation at low voltage and a feedback controlled duty cycling schemecan reduce power.

The amplifier 105 for the XTAL 106 can meet the Barkhausen oscillationcriterion at low voltage to ensure oscillation of the XTAL. Variousinverting amplifier architectures can be used to implement theamplifier. A simple push-pull inverter (a digital inverter) with a bigbias resistor 107 shown in FIG. 1 can be used: for example, it is singlestage and consumes less power. W. Thommen, “An improved Low PowerCrystal Oscillator,” IEEE European Solid State Circuits Conference,1999. Sizing the driver to maintain the correct negative resistance atlow supply voltage can be a challenge. At lower driver strength (smallersizes for nMOS and pMOS), the negative resistance 108 of the amplifier105 is lower and cannot meet the oscillation criterion. Increasing thedriver transistor sizes increases the negative resistance, but thenegative resistance starts decreasing again at some point withincreasing size because of the self-loading in the inverter. Also,increasing the size of the inverter increases the power consumption.

Open loop sizing of the amplifier 105 is unlikely to produce afunctioning XTAL circuit 101 with high yield in sub-threshold regime dueto the impact of process variations, which have an exponential impact onthe transistor resistance in this operating region. To support operationat low voltage, some embodiments disclosed herein use a calibrationmethod to address this variation. FIG. 2 shows a block diagram of afeedback scheme that uses information from the output of a XTAL driver201 (the XTAL 204 may or may not be attached and oscillating) operatingat low voltage, including into the sub-threshold regime, to adjust thecircuit level properties of the XTAL driver 201 such that its negativeresistance is calibrated to the correct (or desired or predefined)value. For example, the feedback circuit includes a feedback controlunit 202 that receives the driver output 203 from the XTAL driver 201.The driver output 203 can be used by the feedback control unit 202 todetermine the current status of the oscillation, e.g., amplitudes of theoscillation, power consumption, etc. The feedback control unit 202 canthen send a signal to the XTAL driver 201 to tune the XTAL driver 201 toset negative resistance for sub-threshold operation of the XTAL 204,e.g., at 205.

FIG. 3 shows a block diagram of circuit implementation of a feedbacksystem using the calibration scheme shown in FIG. 2 for sub-thresholdoperation regime of a XTAL, according to an embodiment. As shown in FIG.3, the output 302 of the inverter 301 can be sent to a feedback controlunit 303 (e.g., which could be the equivalent of 202 in FIG. 2) used toset or generate a feedback control signal that tunes the MOS transistorstrength to adjust the resistance of the inverter, e.g., at 304.

FIG. 4 shows a system block diagram of an alternative circuitimplementation of the feedback system for sub-threshold operation of aXTAL as shown in FIG. 2, e.g., by connecting the inverter output 402 toan off-chip resistor 404 with a reference value of resistance, accordingto an embodiment. The inverter output 402 is compared to a voltagereference 405 and the result is used by the feedback control unit 403(e.g., equivalent to 202 in FIG. 2) to set (or generate) a controlsignal that adjusts the effective lengths of the MOS transistors of theinverter 401, e.g., at 406. A similar scheme could use an on-chipresistance for calibration.

FIG. 5 shows a more detailed circuit schematic of an example of thecalibration scheme shown in FIG. 4 to set the drive strength of theamplifier transistors MP 502 a and MN 502 b. The amplifier 501 isenabled when ENP (503 b)=0 and ENN (503 a)=1. For calibration of MN 502b to a given drive strength, ENN 503 a and ENP 503 b are set to one.This enables the calibration circuit and connects MN 502 b to anexternal resistor Rc 505 through the switch MNC 504. Oscillating signalXI 506 (e.g., equivalent to 103 in FIG. 1) to the amplifier 501 isconnected to Ref 508, which is selected to be at V_(DD)/2 to tune for abalanced inverter voltage transfer characteristic. The size oftransistor MN 502 b is changed using the successive approximationregister (SAR) 509 logic and the comparator 510 in the feedback loop.This can happen in the following way. Oscillating signal XI 506 and Ref508 are set to V_(DD)/2, and the pull-down path is enabled while thepull-up path is disabled. The external resistor Rc 505 is connected toV_(DD). If the size of MN 502 b is very big, then it will pull down theXO node 512 below Ref 508, which will cause the comparator output to golow. This low signal causes the SAR logic 509 to reduce the size of thetransistor MN 502 b. The size of MN 502 b is successively approximatedby turning on or off different fingers of the transistor MN 502 b thatare binary weighted in size. In this embodiment, the process takes 5clock cycles, and the algorithm effectively performs a binary search forthe right drive strength of the transistor MN 502 b set by the externalresistor Rc 505. This calibrates MN 502 b to the right drive strength,compensating for process variation. Similarly MP 502 a is sized bysetting ENN 503 a and ENP 503 b to zero and connecting the externalresistor Rc 505 to ground. The size of the external resistor Rc 505 canbe used so that the amplifier 501 can be sized to supply 5-20 nA of biascurrent, which provides enough drive strength to meet Barkhausencriteria for oscillation.

FIG. 6 shows a simulation result of an example of the oscillator aftercalibration (as implemented in various embodiments illustrated in FIGS.3-5), confirming that it can oscillate at a V_(DD) of 0.3V at a powerconsumption of ˜2 nW.

As discussed below, in addition to or alternative to biasing theamplifier for sub-threshold operation, a feedback controlled dutycycling of the oscillator can be used to measure traits of the XTAL tomaintain the oscillation while reducing power. The energy of a crystaloscillator is stored in its equivalent inductor and capacitor. After thesaturation of oscillation, the stored energy in crystal's equivalentinductor and capacitor is saturated. If the amplifier is disabled inthis condition, the oscillation will start decaying. The powerconsumption becomes negligible when the oscillator is disabled. Theoscillation does not die right away but instead decays with a timeconstant given by ESR (e.g., 111 in FIG. 1) and Lm (series inductance,e.g., 109 in FIG. 1) of the crystal. The output of the crystaloscillator is still useful and can be used to provide clock when theoutput of the crystal oscillator is decaying because the frequency ofthe output of the crystal oscillator does not drift while the amplitudedecays. Therefore, power consumption of crystal oscillator can befurther reduced by switching off the amplifier. If the amplitude of thecrystal oscillator output is allowed to decrease too far, theoscillation stops, so the amplifier can be turned back on before theoscillation decays too far.

FIG. 7 shows a system block diagram for a XTAL driver 703 and anoscillation control 705 (e.g., similar to the feedback control unit 202in FIG. 2) that uses feedback from the oscillating signal(s) X_(I) 701and/or X_(O) 700 to turn on and off the driver 703 for saving power. Thefeedback The XTAL driver 703 generates a duty cycle signal to modulatean envelope of the oscillation at XTAL 702; and an oscillation controlunit 705 uses feedback from the oscillation X_(I) 701 and/or X_(O) 700to periodically turn on and/or off the XTAL driver 703 such that theXTAL driver can be turned off to save power but to be turned on in timebefore the oscillation stops. For example, as shown in FIG. 7, when theamplifier/driver is enabled (e.g., at 706), the amplitude of theenvelope of the oscillation 706 increases; and when the amplifier/driveris disabled (e.g., at 707), the amplitude of the oscillation envelope706 decreases. Thus, to both save power and sustain the oscillation, theoscillation control unit 705 uses feedback information related to theamplitude of the oscillating signal envelope (e.g., 701 and 700) toensure the XTAL driver 703 turns back on in time to preserveoscillation, e.g., turning on the amplifier/XTAL driver 703 when theamplitude of the envelope of the oscillation decays to a minimum value(e.g., 709) and turning off the amplifier/XTAL driver 703 when theamplitude of the envelope of the oscillation reaches a maximum value(e.g., 708). In this way, the amplitudes of the envelope of the XTALoscillation may oscillate between the minimum value 709 and the maximumvalue 708 so that the XTAL oscillation can be maintained.

FIG. 8 shows a system block diagram and a timing diagram for a systemand scheme that uses feedback to duty cycle the XTAL amplifier for powersavings while ensuring that the oscillation remains intact, according toan embodiment. The amplifier 801 is switched periodically while keepingthe amplitude of oscillation high enough for the receiver circuit todetect oscillation. When the amplifier 801 is disabled (e.g., at 806),the oscillation at X_(I) 802 will decay with a time constant (T_(D))807, which is determined by the ESR (e.g., 111 in FIG. 1) and Lm (e.g.,109 in FIG. 1). When the amplifier 801 is enabled again during 808, theamplitude of the XTAL oscillation grows with a time constant (T_(G))809, which is determined by R_(N)—ESR and Lm. A. Shrivastava, R. Yadav,and P. K. Rana, “Fast Start-up Crystal Oscillator,” U.S. Pat. No.8,120,439, which is incorporated by reference. For optimal powersavings, the amplifier 801 should be disabled for time proportional toT_(D) 807 and enabled for time proportional to T_(G) 809 as shown inFIG. 8. Other control scheme embodiments are possible, including directcomparison of the oscillation envelope amplitude or maximum/minimumvalues with voltage references.

The feedback control unit (labeled “OSC T_(ON) and T_(OFF) Control”) 803in FIG. 8 measures T_(G) and T_(D). A counter running based on theoscillator output frequency is enabled when the amplitude of the crystaloscillator (XTAL) output crosses a set threshold. The counter countsuntil C1 and stops when the amplitude of the crystal oscillator outputcrosses a higher threshold. This results in a digital output pulseproportional to T_(G). Similarly, a pulse with width C2 proportional toT_(D) can be obtained. The feedback circuit can produce a clock with theperiod (C1+C2), with C1 as the high phase width and C2 as the low phasewidth, as shown in FIG. 8. The proposed technique enables a calibratedswitching of the amplifier 801 of the crystal oscillator XTAL andreduces the power to near 1 nW or below.

FIG. 9 shows a circuit to measure T_(G) (e.g., the circuitimplementation may be part of the oscillation control unit 803 in FIG.8) and a timing diagram showing the growing amplitude of the envelope ofXTAL oscillation, according to an embodiment. The circuit includescomparators 901 a-b and SR flip-flops 902 a-b. Threshold voltagesV_(REFH) 905 a (e.g., 220 mV for V_(DD)=0.3V) and V_(REFL) 905 b (e.g.,200 mV for V_(DD)=0.3V) are applied at the negative terminal of therespective comparator, while X_(I) is applied at the positive terminalof each comparator. Once the oscillation's amplitude goes aboveV_(REFL), the output of the upper comparator 901 a goes high, and thecorresponding SR flip-flop 902 a is set. This sets CountEn 906 to high.A counter (not shown) is enabled using this signal, and the counterstarts counting. The amplitude of oscillation continues increasing. Oncethe oscillation crosses V_(REFH) 905 a, the lower comparator 901 b goeshigh, the corresponding SR flip-flop 902 b is set and sets CountEn 906is set to zero. This stops the counter and sets the value of thecounter, which is proportional to the growth of oscillation. The valueof the counter is digital and is stored, while the circuit in FIG. 9 isdisabled to save power. The proposed circuit consumes power only whenthe count value is needed.

FIG. 10 shows the circuit implementation for obtaining T_(D) for theoscillator (e.g., the circuit implementation may be part of theoscillation control unit 803 in FIG. 8) and a timing diagram showing thedecaying amplitude of the envelope of XTAL oscillation, according to anembodiment. The circuit in FIG. 10 is very similar to the circuit usedfor obtaining T_(G) shown in FIG. 9, except that two additional Dflip-flops 1002 a-b are included to capture negative triggers. Forexample, when the oscillation's amplitude decays below V_(REFH) (1005a), the output of the lower comparator 1001 b goes low, and thecorresponding SR flip-flop 1003 b is set and thus the D flip-flop 1002 ais set high. This sets CountEn 906 to high to enable a counter to startcounting. When the amplitude of oscillation continues decaying andcrosses V_(REFL) 1005 b, the upper comparator 1001 a goes low, and thusthe corresponding SR flip-flop 1003 a is set, and the D flip-flop 1002 ahas a same output value as that of 1002 b. This way, CountEn 906 is setto zero. This stops the counter and sets the value of the counter, whichis proportional to the decay of oscillation.

It also enables a counter that counts when X_(I) is between V_(REFH)1005 a and V_(REFL) 1005 b. While T_(G) (e.g., 809 in FIG. 8) isobtained when the amplifier (e.g., 801 in FIG. 8) is enabled, T_(D)(e.g., 807 in FIG. 8) is obtained when the amplifier (e.g., 801 in FIG.8) is disabled. Both T_(G) and T_(D) are stored digitally and theircorresponding circuits are disabled to save power. After obtaining T_(G)and T_(D), the oscillator control (e.g., 803 in FIG. 8) turns on theamplifier (e.g., 801 in FIG. 8) for a time proportional to T_(D) andturns it off for a time proportional to T_(G). This duty cycling of theamplifier saves power, and the feedback scheme protects the oscillationand ensures the oscillation remains intact. The total power consumptioncan be, for example, goes below 1 nW.

FIG. 11 shows the complete circuit diagram of an example of the proposedcrystal oscillator circuit (e.g., a circuit implementation of the XTALcircuit shown in FIGS. 7-8). First, the calibration of the amplifier(e.g., 801 in FIG. 8) is performed at a calibration circuit 1101. Thecalibration of the amplifier can be performed once after manufacturingor more often to compensate for environmental changes, for example. Thecalibration circuit 1101 sets the drive strength of the amplifier andcompensates for process variations or other variations. Aftercalibration, the time constant generation circuit 1102 obtains the timeof growth T_(G) and time of decay T_(D) of the oscillator. These timeconstants are used to configure the clock, DCCLK 1103, to switch theamplifier on and off. The duty cycle of DCCLK 1103 is determined byT_(G) and T_(D) with high time=T_(G) and low time=T_(D). Once the DCCLK1103 is configured, the time constant generation circuit 1102 isdisabled. Similarly, calibration circuit 1101 is disabled aftercalibration, and all the digital bits are stored. This eliminates thepower overhead of the calibration circuit 1101 or time constantgeneration circuit 1102. The power consumption is given by the amplifierwith duty cycling. A clock buffer 1105 is used to level convert theclock to higher voltage if needed.

FIG. 12 shows an example of the simulated results of the XTAL driver,e.g., showing duty cycling of the XTAL amplifier, leading to the sawtoothed envelope for the oscillating signal output and saving power. Theexample XTAL driver in FIG. 12 was implemented in a 130 nm commercialCMOS process and fabricated. The waveform shows successful operation ofthe circuit at an average power consumption of less than 1 nW and afrequency of 32.768 kHz. For example, chart 1201 shows oscillation withduty cycling of the amplitude, and chart 1202 shows periodic enablingsignal (e.g., DCCLK 1103 in FIG. 11) for the XTAL amplifier duringoscillation duty cycling.

FIG. 13 shows a flowchart for calibrating an XTAL driver for operationat low voltage including the sub-threshold region (e.g., as performed bythe feedback control unit 202 in FIG. 2), according to an embodiment. Afeedback control unit can be included in the XTAL circuit to bias theXTAL driver at a low voltage that may be sub-threshold at 1301, e.g.,see the feedback control unit 202 in FIG. 2. The feedback control unitcan configure any load components of the feedback circuit (e.g., seeFIG. 2) that are used for measurement of the properties of the XTALdriver, at 1302, and then measure circuit properties of the XTAL driverthat influence the negative resistance, at 1303, e.g., voltage, current,and/or the like. The feedback control unit may repeat as needed forother driver properties, at 1304, steps 1302-1303 to obtain differentdriver properties, e.g., amplitudes of the oscillation, etc. Based onthe measurements, the control feedback unit can tune the XTAL driverthat effects its negative resistance to set the negative resistance forproper oscillation at low voltage, at 1305.

FIG. 14 shows a flowchart for duty cycling the driver for an XTAL whilepersevering oscillation (e.g., as performed by the oscillation controlunit 705 in FIG. 7, or 803 in FIG. 8), according to an embodiment. Asshown in FIG. 14, anoscillation feedback control unit (e.g., 705 in FIG.7; 803 in FIG. 8) may measure the rise and the fall times of the XTALoscillation envelope, at 1401 (e.g., see the rise and the fall of theoscillation envelope in FIGS. 7-8). The oscillation feedback controlunit may initiate the XTAL oscillation and allow the oscillation toincrease in amplitude at 1402, e.g., by reaching a maximum oscillationamplitude (e.g., see 708 in FIG. 7). The feedback control unit may thenturn off the XTAL driver at 1403, so as to save power; and wait a timeproportional to the measured fall time of the oscillation envelope at1404 before turning on the XTAL driver again at 1405. In this way, thefeedback control unit keeps the oscillation before the oscillation stops(e.g., before the amplitude of the oscillation diminishes to zero, or toa sufficiently small value such that a receiver circuit cannot detectthe oscillation, etc.). The control unit may then wait a timeproportional to the measured rise time of the oscillation envelope, at1406, to wait for the amplitude of the oscillation envelope to reach amaximum value. The turning on and off of the XTAL driver may beperformed periodically in a repeated manner at 1407, so as to form aduty cycle to save power and preserve the oscillation.

FIG. 15 shows a flowchart for duty cycling an XTAL while perseveringoscillation (e.g., as performed by the oscillation control unit 705 inFIG. 7, or 803 in FIG. 8), according to another embodiment. Similar tothe work flow described in FIG. 14, a feedback control unit may initiatethe XTAL oscillation and allow the oscillation to increase in amplitudeat 1501, and may turn off the XTAL driver at 1502 to save power. Thecontrol unit may then measure the XTAL envelope until the XTALoscillation envelope reaches a threshold in range or extrema at 1503,e.g., the minimum value 709 in FIG. 7, and then turn on the XTAL driverat 1504. The control unit may then measure the XTAL envelope until itreaches a maximum threshold in range or extrema, at 1505, e.g., themaximum value 708 in FIG. 7. The control unit may then monitor the XTALoscillation and repeatedly turn off/on the XTAL driver as in steps1502-1505.

In sum, in some embodiments, the amplifier for an XTAL is biased in thesub-threshold operating regime. In addition or alternatively, a feedbackcontrol scheme can be used to bias an amplifier for an XTAL biased inthe sub-threshold operating regime.

In some embodiments, the amplifier of a XTAL oscillator can be dutycycled to save power while the amplitude of the XTAL oscillation startsto decay but the amplifier can be turned back on to maintain theoscillation before it stops. In addition or alternatively, a feedbackcontrol scheme to duty cycle the amplifier of a XTAL oscillator can beused to save power while the amplitude of the XTAL oscillation starts todecay and the amplifier can be turned back on to maintain theoscillation before it stops.

It is intended that some of the methods and apparatus described hereincan be performed by software (stored in memory and executed onhardware), hardware, or a combination thereof. For example, the controlcircuits discussed above can alternatively be control modules or controldevices implemented in or including such software and/or hardware.Hardware modules may include, for example, a general-purpose processor,a field programmable gate array (FPGA), and/or an application specificintegrated circuit (ASIC). Software modules (executed on hardware) canbe expressed in a variety of software languages (e.g., computer code),including C, C++, Java™, Ruby, Visual Basic™, and other object-oriented,procedural, or other programming language and development tools.Examples of computer code include, but are not limited to, micro-code ormicro-instructions, machine instructions, such as produced by acompiler, code used to produce a web service, and files containinghigher-level instructions that are executed by a computer using aninterpreter. Additional examples of computer code include, but are notlimited to, control signals, encrypted code, and compressed code.

Some embodiments described herein relate to a computer storage productwith a non-transitory computer-readable medium (also can be referred toas a non-transitory processor-readable medium) having instructions orcomputer code thereon for performing various computer-implementedoperations. The computer-readable medium (or processor-readable medium)is non-transitory in the sense that it does not include transitorypropagating signals per se (e.g., a propagating electromagnetic wavecarrying information on a transmission medium such as space or a cable).The media and computer code (also can be referred to as code) may bethose designed and constructed for the specific purpose or purposes.Examples of non-transitory computer-readable media include, but are notlimited to, magnetic storage media such as hard disks, floppy disks, andmagnetic tape; optical storage media such as Compact Disc/Digital VideoDiscs (CD/DVDs), Compact Disc-Read Only Memories (CD-ROMs), andholographic devices; magneto-optical storage media such as opticaldisks; carrier wave signal processing modules; and hardware devices thatare specially configured to store and execute program code, such asApplication-Specific Integrated Circuits (ASICs), Programmable LogicDevices (PLDs), Read-Only Memory (ROM) and Random-Access Memory (RAM)devices.

While various embodiments have been described above, it should beunderstood that they have been presented by way of example only, and notlimitation. Where methods and steps described above indicate certainevents occurring in certain order, the ordering of certain steps may bemodified. Additionally, certain steps may be performed concurrently in aparallel process when possible, as well as performed sequentially asdescribed above. Although various embodiments have been described ashaving particular features and/or combinations of components, otherembodiments are possible having any combination or sub-combination ofany features and/or components from any of the embodiments describedherein.

What is claimed is:
 1. An apparatus, comprising: a crystal oscillator(XTAL) configured to generate an XTAL oscillation; and a time constantgeneration circuit operatively coupled to the XTAL, the time constantgeneration circuit including: a first comparator configured to set ahigh value for a counter to start counting when an amplitude of the XTALoscillation crosses a first threshold voltage, and a second comparatorconfigured to set a zero value for the counter to stop counting when theamplitude of the XTAL oscillation crosses a second threshold voltage, acount of the counter corresponding to a time constant of the XTALoscillation.
 2. The apparatus of claim 1, wherein: the second thresholdvoltage exceeds the first threshold voltage, and the time constant ofthe XTAL oscillation corresponds to a growth time constant T_(G) of theXTAL oscillation.
 3. The apparatus of claim 1, wherein: the firstthreshold voltage exceeds the second threshold voltage, and the timeconstant of the XTAL oscillation corresponds to a decay time constantT_(D) of the XTAL oscillation.
 4. The apparatus of claim 1, furthercomprising: an XTAL driver operatively coupled to the XTAL and having anamplifier, the counting of the counter occurs when the second thresholdvoltage exceeds the first threshold voltage and when the amplifier isenabled.
 5. The apparatus of claim 1, further comprising: an XTAL driveroperatively coupled to the XTAL and having an amplifier, the counting ofthe counter occurs when the first threshold voltage exceeds the secondthreshold voltage and when the amplifier is disabled.
 6. The apparatusof claim 1, further comprising: an XTAL driver operatively coupled tothe XTAL and having an amplifier, the time constant generation circuitfurther including an oscillation control unit configured to duty cyclethe amplifier by repeatedly turning on and off the amplifier so as tosustain the XTAL oscillation.
 7. The apparatus of claim 1, furthercomprising: an XTAL driver operatively coupled to the XTAL and having anamplifier, the time constant generation circuit further including anoscillation control unit configured to duty cycle the amplifier byrepeatedly turning on and off the amplifier so as to sustain the XTALoscillation, when the first threshold voltage exceeds the secondthreshold voltage, the time constant of the XTAL oscillation correspondsto a decay time constant T_(D) of the XTAL oscillation, and theoscillator control unit turns on the amplifier for a time periodproportional to T_(D), and when the second threshold voltage exceeds thefirst threshold voltage, the time constant of the XTAL oscillationcorresponds to a growth time constant T_(G) of the XTAL oscillation, andthe oscillator control unit turns off the amplifier for a time periodproportional to T_(G).
 8. The apparatus of claim 1, further comprising:an XTAL driver operatively coupled to the XTAL and having an amplifier;and a calibration circuit operatively coupled to the XTAL driver andconfigured to set a drive strength of the amplifier.
 9. A method,comprising: initiating a crystal oscillator (XTAL) oscillation of anXTAL; setting a high value for a counter to start counting when anamplitude of the XTAL oscillation crosses a first threshold voltage;setting a zero value for the counter to stop counting when the amplitudeof the XTAL oscillation crosses a second threshold voltage; andidentifying a count of the counter to correspond to a time constant ofthe XTAL oscillation.
 10. The method of claim 9, wherein: the secondthreshold voltage exceeds the first threshold voltage, and the timeconstant of the XTAL oscillation corresponds to a growth time constantT_(G) of the XTAL oscillation.
 11. The method of claim 9, wherein: thefirst threshold voltage exceeds the second threshold voltage, and thetime constant of the XTAL oscillation corresponds to a decay timeconstant T_(D) of the XTAL oscillation.
 12. The method of claim 9,wherein the counting of the counter occurs when the second thresholdvoltage exceeds the first threshold voltage and when an amplifier of anXTAL driver that is operatively coupled to the XTAL is enabled.
 13. Themethod of claim 9, wherein the counting of the counter occurs when thefirst threshold voltage exceeds the second threshold voltage and when anamplifier of an XTAL driver that is operatively coupled to the XTAL isdisabled.
 14. A method, comprising: obtaining a growth time constantT_(G) and a decay time constant T_(D) of a crystal oscillator (XTAL)oscillation of an XTAL from a time constant generation circuit;configuring a control clock to duty cycle an XTAL driver by repeatedlyswitching an amplifier of the XTAL driver on and off for time periodssubstantially equal to T_(G) and T_(D), respectively, the XTAL driveroperatively coupled to the XTAL; disabling the time constant generationcircuit after configuring the control clock; and duty cycling theamplifier using the control clock so as to sustain the XTAL oscillationafter disabling the time constant generation circuit.
 15. The method ofclaim 14, further comprising: setting a drive strength of the amplifierof the XTAL driver so as to compensate for process variations.
 16. Themethod of claim 14, further comprising: setting a drive strength of theamplifier of the XTAL driver using a calibration circuit; and disablingthe calibration circuit prior to duty cycling the amplifier.
 17. Themethod of claim 14, wherein obtaining a growth time constant T_(G)includes: setting a high value for a counter to start counting when anamplitude of the XTAL oscillation crosses a first threshold voltage;setting a zero value for a counter to start counting when an amplitudeof the XTAL oscillation crosses a second threshold voltage that exceedsthe first threshold voltage; and identifying a count of the counter tocorrespond to the growth time constant T_(G) of the XTAL oscillation.18. The method of claim 14, wherein obtaining a decay time constantT_(D) includes: setting a high value for a counter to start countingwhen an amplitude of the XTAL oscillation crosses a first thresholdvoltage; setting a zero value for a counter to start counting when anamplitude of the XTAL oscillation crosses a second threshold voltagethat is less than the first threshold voltage; and identifying a countof the counter to correspond to the decay time constant T_(G) of theXTAL oscillation.
 19. The method of claim 14, further comprising:biasing the amplifier so as to facilitate operation of the amplifier ina sub-threshold operating regime of metal-oxide-semiconductor (MOS)transistors of the amplifier.
 20. The method of claim 14, furthercomprising: tuning a transistor strength of an inverter of the amplifierso as to facilitate operation of the amplifier in a sub-thresholdoperating regime of MOS transistors of the amplifier.